public override void Split(TreeNode twoFourNode, int element)
{
TwoFourTreeNode p;
twoFourNode = (TwoFourTreeNode) twoFourNode;
if (twoFourNode.parent == null)
{
p = new TwoFourTreeNode();
}
else
{
p = (TwoFourTreeNode) twoFourNode.parent;
}
TwoFourTreeNode n1 = new TwoFourTreeNode();
TwoFourTreeNode n2 = new TwoFourTreeNode();
int[] elements = { element, twoFourNode.elements[0], twoFourNode.elements[1], twoFourNode.elements[2] };
int middle;
this.SortElements(elements, elements.Length);
n1.elements[0] = elements[0];
n1.elements[1] = elements[1];
n2.elements[0] = elements[3];
middle = elements[2];
n1.parent = p;
n2.parent = p;
if (p.NumberOfElements() == 0)
{
p.children[0] = n1;
p.children[1] = n2;
this.root = p;
}
else if (p.NumberOfElements() == 1)
{
if (n2.elements[0] < p.elements[0])
{
p.children[2] = p.children[1];
p.children[0] = n1;
p.children[1] = n2;
}
else
{
p.children[1] = n1;
p.children[2] = n2;
}
}
else if (p.NumberOfElements() == 2)
{
if (n2.elements[0] < p.elements[0] && n2.elements[0] < p.elements[1])
{
p.children[3] = p.children[2];
p.children[2] = p.children[1];
p.children[0] = n1;
p.children[1] = n2;
}
else if (n1.elements[1] > p.elements[0] && n1.elements[1] > p.elements[1])
{
p.children[2] = n1;
p.children[3] = n2;
}
else
{
p.children[3] = p.children[2];
p.children[1] = n1;
p.children[2] = n2;
}
}
else if (p.NumberOfElements() == 3)
{
if (n2.elements[0] < p.elements[0])
{
p.children[4] = p.children[3];
p.children[3] = p.children[2];
p.children[2] = p.children[1];
p.children[1] = n2;
p.children[0] = n1;
}
else if (n1.elements[0] > p.elements[0] && n2.elements[0] < p.elements[1])
{
p.children[4] = p.children[3];
p.children[3] = p.children[2];
p.children[2] = n2;
p.children[1] = n1;
}
else if (n1.elements[0] > p.elements[1] && n2.elements[0] < p.elements[2])
{
p.children[4] = p.children[3];
p.children[3] = n2;
p.children[2] = n1;
}
else
{
p.children[3] = n1;
p.children[4] = n2;
}
}
//if it is not a leaf check
if (twoFourNode.IsLeaf() == false)
{
twoFourNode.children[0].parent = n1;
twoFourNode.children[1].parent = n1;
twoFourNode.children[2].parent = n1;
twoFourNode.children[3].parent = n2;
twoFourNode.children[4].parent = n2;
n1.children[0] = twoFourNode.children[0];
n1.children[1] = twoFourNode.children[1];
n1.children[2] = twoFourNode.children[2];
n2.children[0] = twoFourNode.children[3];
n2.children[1] = twoFourNode.children[4];
}
if (p.NumberOfElements() == 3)
{
this.Split(p, middle);
}
else if (p.NumberOfElements() < this.limit)
{
p.elements[p.NumberOfElements()] = middle;
this.SortElements(p.elements, p.NumberOfElements());
}
}
//Tries to insert the elements, if not returns false
public bool TryInsert(TreeNode treeNode, int element)
{
bool result = true;
//If it is root just add the element to the root
if (treeNode.NumberOfElements() == 0 && treeNode.parent == null)
{
treeNode.elements[0] = element;
}
else if (treeNode.NumberOfElements() < this.limit)
{
treeNode.elements[treeNode.NumberOfElements()] = element;
this.SortElements(treeNode.elements, treeNode.NumberOfElements());
}
else
{
result = false;
}
return result;
}
public TreeNode parent; //parent node
#endregion Fields
#region Constructors
//in case this node isn't a leaf, numberOfElement + 1 gives the number of children
public TreeNode()
{
this.parent = null;
}
public void TakeElementFromNextRightSibling(TreeNode p, TreeNode node, int n)
{
node.elements[0] = p.elements[n];
p.elements[n] = p.children[n + 1].elements[0];
if (this.limit == 2)
{
p.children[n + 1].elements[0] = p.children[n + 1].elements[1];
p.children[n + 1].elements[1] = 0;
}
else
{
p.children[n + 1].elements[0] = p.children[n + 1].elements[1];
p.children[n + 1].elements[1] = p.children[n + 1].elements[2];
p.children[n + 1].elements[2] = 0;
}
if (node.IsLeaf() == false)
{
node.children[1] = p.children[n + 1].children[0];
if (this.limit == 2)
{
p.children[n + 1].children[0] = p.children[n + 1].children[1];
p.children[n + 1].children[1] = p.children[n + 1].children[2];
p.children[n + 1].children[2] = null;
}
else
{
p.children[n + 1].children[0] = p.children[n + 1].children[1];
p.children[n + 1].children[1] = p.children[n + 1].children[2];
p.children[n + 1].children[2] = p.children[n + 1].children[3];
p.children[n + 1].children[3] = null;
}
node.children[1].parent = node;
}
}
public void TakeElementFromTwoNextRightSibling(TreeNode p, TreeNode node, int n)
{
node.elements[0] = p.elements[n];
p.elements[n] = p.children[n + 1].elements[0];
p.children[n + 1].elements[0] = p.elements[n + 1];
p.elements[n + 1] = p.children[n + 2].elements[0];
if (p.children[n + 2].NumberOfElements() == 2)
{
p.children[n + 2].elements[0] = p.children[n + 2].elements[1];
p.children[n + 2].elements[1] = 0;
}
else if (p.children[n + 2].NumberOfElements() == 3)
{
p.children[n + 2].elements[0] = p.children[n + 2].elements[1];
p.children[n + 2].elements[1] = p.children[n + 2].elements[2];
p.children[n + 2].elements[2] = 0;
}
if (node.IsLeaf() == false)
{
node.children[1] = p.children[n + 1].children[0];
p.children[n + 1].children[0] = p.children[n + 1].children[1];
p.children[n + 1].children[1] = p.children[n + 2].children[0];
if (p.children[n + 2].NumberOfElements() == 1)
{
p.children[n + 2].children[0] = p.children[n + 2].children[1];
p.children[n + 2].children[1] = p.children[n + 2].children[2];
p.children[n + 2].children[2] = null;
}
else if (p.children[n + 2].NumberOfElements() == 2)
{
p.children[n + 2].children[0] = p.children[n + 2].children[1];
p.children[n + 2].children[1] = p.children[n + 2].children[2];
p.children[n + 2].children[2] = p.children[n + 2].children[3];
p.children[n + 2].children[3] = null;
}
node.children[1].parent = node;
p.children[n + 1].children[1].parent = p.children[n + 1];
}
}
public void Merge(TreeNode node)
{
if (node.parent.NumberOfElements() == 1)
{
//empty node at the left
if (node.parent.children[0] == node)
{
node.parent.children[1].elements[1] = node.parent.children[1].elements[0];
node.parent.children[1].elements[0] = node.parent.elements[0];
node.parent.elements[0] = 0;
//remove the node
node.parent.children[0] = node.parent.children[1];
node.parent.children[1] = null;
//if node is internal
if (node.IsLeaf() == false)
{
node.parent.children[0].children[2] = node.parent.children[0].children[1];
node.parent.children[0].children[1] = node.parent.children[0].children[0];
node.parent.children[0].children[0] = node.children[0];
//update the parent
node.parent.children[0].children[0].parent = node.parent.children[0];
}
}
//empty node at the right
else
{
node.parent.children[0].elements[1] = node.parent.elements[0];
node.parent.elements[0] = 0;
node.parent.children[1] = null;
//if node is internal
if (node.IsLeaf() == false)
{
node.parent.children[0].children[2] = node.children[0];
node.parent.children[0].children[2].parent = node.parent.children[0];
}
}
}
else if (node.parent.NumberOfElements() == 2)
{
//empty node at the left
if (node.parent.children[0] == node)
{
node.parent.children[1].elements[1] = node.parent.children[1].elements[0];
node.parent.children[1].elements[0] = node.parent.elements[0];
node.parent.elements[0] = node.parent.elements[1];
node.parent.elements[1] = 0;
node.parent.children[0] = node.parent.children[1];
node.parent.children[1] = node.parent.children[2];
node.parent.children[2] = null;
//if node is internal
if (node.IsLeaf() == false)
{
node.parent.children[0].children[2] = node.parent.children[0].children[1];
node.parent.children[0].children[1] = node.parent.children[0].children[0];
node.parent.children[0].children[0] = node.children[0];
node.parent.children[0].children[0].parent = node.parent.children[0];
}
}
//empty node at the middle
else if (node.parent.children[1] == node)
{
node.parent.children[0].elements[1] = node.parent.elements[0];
node.parent.elements[0] = node.parent.elements[1];
node.parent.elements[1] = 0;
node.parent.children[1] = node.parent.children[2];
node.parent.children[2] = null;
//if node is internal
if (node.IsLeaf() == false)
{
node.parent.children[0].children[2] = node.children[0];
node.parent.children[0].children[2].parent = node.parent.children[0];
}
}
//empty node at the right
else
{
node.parent.children[1].elements[1] = node.parent.elements[1];
node.parent.elements[1] = 0;
node.parent.children[2] = null;
//if node is internal
if (node.IsLeaf() == false)
{
node.parent.children[1].children[2] = node.children[0];
node.parent.children[1].children[2].parent = node.parent.children[1];
}
}
}
else if (node.parent.NumberOfElements() == 3)
{
if (node.parent.children[0] == node)
{
node.parent.children[1].elements[1] = node.parent.children[1].elements[0];
node.parent.children[1].elements[0] = node.parent.elements[0];
node.parent.elements[0] = node.parent.elements[1];
node.parent.elements[1] = node.parent.elements[2];
node.parent.elements[2] = 0;
node.parent.children[0] = node.parent.children[1];
node.parent.children[1] = node.parent.children[2];
node.parent.children[2] = node.parent.children[3];
node.parent.children[3] = null;
//if node is internal
if (node.IsLeaf() == false)
{
node.parent.children[0].children[2] = node.parent.children[0].children[1];
node.parent.children[0].children[1] = node.parent.children[0].children[0];
node.parent.children[0].children[0] = node.children[0];
node.parent.children[0].children[0].parent = node.parent.children[0];
}
}
else if (node.parent.children[1] == node)
{
node.parent.children[0].elements[1] = node.parent.elements[0];
node.parent.elements[0] = node.parent.elements[1];
node.parent.elements[1] = node.parent.elements[2];
node.parent.elements[2] = 0;
node.parent.children[1] = node.parent.children[2];
node.parent.children[2] = node.parent.children[3];
node.parent.children[3] = null;
//if node is internal
if (node.IsLeaf() == false)
{
node.parent.children[0].children[2] = node.children[0];
node.parent.children[0].children[2].parent = node.parent.children[0];
}
}
else if (node.parent.children[2] == node)
{
node.parent.children[1].elements[1] = node.parent.elements[1];
node.parent.elements[1] = node.parent.elements[2];
node.parent.elements[2]= 0;
node.parent.children[2] = node.parent.children[3];
node.parent.children[3] = null;
//if node is internal
if (node.IsLeaf() == false)
{
node.parent.children[1].children[2] = node.children[0];
node.parent.children[1].children[2].parent = node.parent.children[1];
}
}
else if (node.parent.children[3] == node)
{
node.parent.children[2].elements[1] = node.parent.elements[2];
node.parent.elements[2] = 0;
node.parent.children[3] = null;
//if node is internal
if (node.IsLeaf() == false)
{
node.parent.children[2].children[2] = node.children[0];
node.parent.children[2].children[2].parent = node.parent.children[2];
}
}
}
}
public virtual void Split(TreeNode treeNode, int element)
{
Console.WriteLine("This method should be overrided");
}
public TreeNode InOrderSuccessor(int element, TreeNode node)
{
TreeNode next;
// When this method is called, key will equal smallValue or largeValue, and we must do a comparison.
// We check if location is a three node and, if it is, we compare key to smallValue. If equal, go down middleChild.
if (node.children[0] != null && node.children[1] != null && node.children[2] != null && node.children[3] != null)
{
if (node.elements[0] == element)
{
next = node.children[1];
}
else if (node.elements[1] == element)
{
next = node.children[2];
}
else
{
next = node.children[3];
}
}
else if (node.children[0] != null && node.children[1] != null && node.children[2] != null)
{
if (node.elements[0] == element)
{
next = node.children[1];
}
else
{
next = node.children[2];
}
}
else
{
next = node.children[1];
}
// Continue down left branches until we encounter a leaf.
while (next.IsLeaf() == false)
{
next = next.children[0];
}
return next;
}
//Look for the right or the closest siblings with two or three elements, if not returns -1
public int HasChildWithTwoElement(TreeNode node)
{
int result = -1;
//check the number of the children equality to 2
if (node.NumberOfElements() == 1)
{
for (int i = 0; i < node.children.Length; i++)
{
if (node.children[i] != null)
{
if (node.children[i].NumberOfElements() == 2 || node.children[i].NumberOfElements() == 3)
{
result = i;
result = result + node.children[i].NumberOfElements() * 10;
break;
}
}
}
}
//number of the children equality to 3
else if (node.NumberOfElements() == 2)
{
if (node.children[0].NumberOfElements() == 0)
{
for (int i = 0; i < node.children.Length; i++)
{
if (node.children[i] != null)
{
if (node.children[i].NumberOfElements() == 2 || node.children[i].NumberOfElements() == 3)
{
result = i;
result = result + node.children[i].NumberOfElements() * 10;
break;
}
}
}
}
// I should take from the right first so the loop counter is decreasing
else
{
for (int i = node.children.Length - 1; i >= 0; i--)
{
if (node.children[i] != null)
{
if (node.children[i].NumberOfElements() == 2 || node.children[i].NumberOfElements() == 3)
{
result = i;
result = result + node.children[i].NumberOfElements() * 10;
break;
}
}
}
}
}
//number of the children equality to 4
else if (node.NumberOfElements() == 3)
{
if (node.children[0].NumberOfElements() == 0)
{
for (int i = 0; i < node.children.Length; i++)
{
if (node.children[i] != null)
{
if (node.children[i].NumberOfElements() == 2 || node.children[i].NumberOfElements() == 3)
{
result = i;
result = result + node.children[i].NumberOfElements() * 10;
break;
}
}
}
}
// I should take from the right first so the loop counter is decreasing
else
{
if (node.children[1].NumberOfElements() == 0)
{
//Check for the element at the right first
for (int i = 1; i < node.children.Length; i++)
{
if (node.children[i] != null)
{
if (node.children[i].NumberOfElements() == 2 || node.children[i].NumberOfElements() == 3)
{
result = i;
result = result + node.children[i].NumberOfElements() * 10;
break;
}
}
}
//If doesn't exist in the right look left
if (result == -1)
{
if (node.children[0].NumberOfElements() == 2 || node.children[0].NumberOfElements() == 3)
{
result = node.children[0].NumberOfElements() * 10;
}
}
}
else
{
for (int i = node.children.Length - 1; i >= 0; i--)
{
if (node.children[i] != null)
{
if (node.children[i].NumberOfElements() == 2 || node.children[i].NumberOfElements() == 3)
{
result = i;
result = result + node.children[i].NumberOfElements() * 10;
break;
}
}
}
}
}
}
return result;
}
public TreeNode FindSubtreeLeaf(TreeNode node, int element)
{
if (node.IsLeaf())
return node;
else
{
if (element < node.elements[0])
return this.FindSubtreeLeaf(node.children[0], element);
else if (node.NumberOfElements() == 1 || (element > node.elements[0] && element < node.elements[1]))
return this.FindSubtreeLeaf(node.children[1], element);
else if (node.NumberOfElements() == 2 || (element > node.elements[1] && element < node.elements[2]))
return this.FindSubtreeLeaf(node.children[2], element);
else
return this.FindSubtreeLeaf(node.children[3], element);
}
}
//Recursively split to balance the tree
public override void Split(TreeNode twoThreeNode, int element)
{
TwoThreeTreeNode p;
if (twoThreeNode.parent == null)
{
p = new TwoThreeTreeNode();
}
else
{
p = (TwoThreeTreeNode) twoThreeNode.parent;
}
TwoThreeTreeNode n1 = new TwoThreeTreeNode();
TwoThreeTreeNode n2 = new TwoThreeTreeNode();
//finding the smallest, middle and large elements
int small, middle, large;
if (element < twoThreeNode.elements[0])
{
small = element;
middle = twoThreeNode.elements[0];
large = twoThreeNode.elements[1];
}
else if (element > twoThreeNode.elements[1])
{
small = twoThreeNode.elements[0];
middle = twoThreeNode.elements[1];
large = element;
}
else
{
small = twoThreeNode.elements[0];
middle = element;
large = twoThreeNode.elements[1];
}
//set smallest and largest keys to the n1 and n2 respectively
n1.elements[0] = small;
n2.elements[0] = large;
//Make p the parent node of n1 and n2
n1.parent = p;
n2.parent = p;
if (p.NumberOfElements() == 0)
{
p.children[0] = n1;
p.children[1] = n2;
this.root = p;
n1.isLeaf = true;
n2.isLeaf = true;
}
else if (p.NumberOfElements() == 1)
{
if (n2.elements[0] < p.elements[0])
{
p.children[2] = p.children[1];
p.children[0] = n1;
p.children[1] = n2;
}
else
{
p.children[1] = n1;
p.children[2] = n2;
}
n1.isLeaf = true;
n2.isLeaf = true;
}
else
{
if (n2.elements[0] < p.elements[0] && n2.elements[0] < p.elements[1])
{
p.children[3] = p.children[2];
p.children[2] = p.children[1];
p.children[0] = n1;
p.children[1] = n2;
}
else if (n1.elements[0] > p.elements[0] && n1.elements[0] > p.elements[1])
{
p.children[2] = n1;
p.children[3] = n2;
}
else
{
p.children[3] = p.children[2];
p.children[1] = n1;
p.children[2] = n2;
}
}
//if it is not a leaf check
if (twoThreeNode.IsLeaf() == false)
{
twoThreeNode.children[0].parent = n1;
twoThreeNode.children[1].parent = n1;
twoThreeNode.children[2].parent = n2;
twoThreeNode.children[3].parent = n2;
n1.children[0] = twoThreeNode.children[0];
n1.children[1] = twoThreeNode.children[1];
n2.children[0] = twoThreeNode.children[2];
n2.children[1] = twoThreeNode.children[3];
n1.isLeaf = false;
n2.isLeaf = false;
}
if (p.NumberOfElements() == 2)
{
this.Split(p, middle);
if (n1.children[0] != null || n2.children[0] != null)
{
if (n1.children[0].IsLeaf() || n2.children[0].IsLeaf())
{
n1.isLeaf = false;
n2.isLeaf = false;
}
}
else
{
n1.isLeaf = true;
n2.isLeaf = true;
}
n1.parent.isLeaf = false;
n2.parent.isLeaf = false;
}
else if (p.NumberOfElements() == 1)
{
if (p.elements[0] < middle)
{
p.elements[1] = middle;
}
else
{
p.elements[1] = p.elements[0];
p.elements[0] = middle;
}
}
else
{
p.elements[0] = middle;
}
}
public TreeNode FindNode(TreeNode node, int element)
{
bool isFound = false;
if (node != null)
{
for (int i = 0; i < node.NumberOfElements(); i++)
{
if (node.elements[i] == element)
isFound = true;
}
if (isFound == true)
return node;
else if (node.NumberOfElements() == 1)
{
if (element < node.elements[0])
return FindNode(node.children[0], element);
else
return FindNode(node.children[1], element);
}
else if (node.NumberOfElements() == 2)
{
if (element < node.elements[0])
{
return FindNode(node.children[0], element);
}
else if (element > node.elements[1])
{
return FindNode(node.children[2], element);
}
else
{
return FindNode(node.children[1], element);
}
}
else if (node.NumberOfElements() == 3)
{
if (element < node.elements[0])
{
return FindNode(node.children[0], element);
}
else if (element > node.elements[0] && element < node.elements[1])
{
return FindNode(node.children[1], element);
}
else if (element > node.elements[1] && element < node.elements[2])
{
return FindNode(node.children[2], element);
}
else
{
return FindNode(node.children[3], element);
}
}
}
return null;
}
